The figure below shows
a right triangle ABC with the circles C1, C2, and C3 with diameters AB,
BC, and AC, respectively. C1 and C2 meet at D and DAE and DCF are
isosceles right triangles. C3 meets EF at G and G1. EH is tangent to C1
and FJ is tangent to C2. Circle with center E and radius EH meets the
circle with center F and radius FJ at K and L. If MN is the common external
tangent to C1 and C2, prove that GL = MN.
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